Weak separation properties for self-similar sets
HTML articles powered by AMS MathViewer
- by Martin P. W. Zerner PDF
- Proc. Amer. Math. Soc. 124 (1996), 3529-3539 Request permission
Abstract:
We develop a theory for self-similar sets in $\mathbb R^s$ that fulfil the weak separation property of Lau and Ngai, which is weaker than the open set condition of Hutchinson.References
- Robert B. Ash, Real analysis and probability, Probability and Mathematical Statistics, No. 11, Academic Press, New York-London, 1972. MR 0435320
- Christoph Bandt and Siegfried Graf, Self-similar sets. VII. A characterization of self-similar fractals with positive Hausdorff measure, Proc. Amer. Math. Soc. 114 (1992), no. 4, 995–1001. MR 1100644, DOI 10.1090/S0002-9939-1992-1100644-3
- K. J. Falconer, Dimensions and measures of quasi self-similar sets, Proc. Amer. Math. Soc. 106 (1989), no. 2, 543–554. MR 969315, DOI 10.1090/S0002-9939-1989-0969315-8
- Kenneth Falconer, Fractal geometry, John Wiley & Sons, Ltd., Chichester, 1990. Mathematical foundations and applications. MR 1102677
- Michael Klemm, Symmetrien von Ornamenten und Kristallen, Hochschultext [University Textbooks], Springer-Verlag, Berlin-New York, 1982 (German). MR 663004, DOI 10.1007/978-3-642-68625-2
- K.-S. Lau and S.-M. Ngai, Multifractal measures and a weak separation condition, Adv. Math. (to appear).
- J. Milnor, A note on curvature and fundamental group, J. Differential Geometry 2 (1968), 1–7. MR 232311, DOI 10.4310/jdg/1214501132
- Andreas Schief, Separation properties for self-similar sets, Proc. Amer. Math. Soc. 122 (1994), no. 1, 111–115. MR 1191872, DOI 10.1090/S0002-9939-1994-1191872-1
- N. Smythe, Growth functions and Euler series, Invent. Math. 77 (1984), no. 3, 517–531. MR 759259, DOI 10.1007/BF01388836
- Philip Wagreich, The growth function of a discrete group, Group actions and vector fields (Vancouver, B.C., 1981) Lecture Notes in Math., vol. 956, Springer, Berlin, 1982, pp. 125–144. MR 704992, DOI 10.1007/BFb0101514
Additional Information
- Martin P. W. Zerner
- Affiliation: Departement Mathematik, ETH Zentrum, CH-8092 Zurich, Switzerland
- Email: zerner@math.ethz.ch
- Received by editor(s): April 11, 1995
- Communicated by: Christopher D. Sogge
- © Copyright 1996 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 124 (1996), 3529-3539
- MSC (1991): Primary 54E40, 54H15; Secondary 28A78
- DOI: https://doi.org/10.1090/S0002-9939-96-03527-7
- MathSciNet review: 1343732